Surface Phonon Polariton-Mediated Near-Field Radiative Heat Transfer at Cryogenic Temperatures

Shen Yan, Yuxuan Luan, Ju Won Lim, Rohith Mittapally, Amin Reihani, Zhongyong Wang, Yoichiro Tsurimaki, Shanhui Fan, Pramod Reddy, and Edgar Meyhofer

Phys. Rev. Lett. 131, 196302 – Published 9 November 2023

Abstract

Recent experiments, at room temperature, have shown that near-field radiative heat transfer (NFRHT) via surface phonon polaritons (SPhPs) exceeds the blackbody limit by several orders of magnitude. Yet, SPhP-mediated NFRHT at cryogenic temperatures remains experimentally unexplored. Here, we probe thermal transport in nanoscale gaps between a silica sphere and a planar silica surface from 77–300 K. These experiments reveal that cryogenic NFRHT has strong contributions from SPhPs and does not follow the $T^{3}$ temperature ( $T$ ) dependence of far-field thermal radiation. Our modeling based on fluctuational electrodynamics shows that the temperature dependence of NFRHT can be related to the confinement of heat transfer to two narrow frequency ranges and is well accounted for by a simple analytical model. These advances enable detailed NFRHT studies at cryogenic temperatures that are relevant to thermal management and solid-state cooling applications.

Received 13 March 2023
Accepted 11 September 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.196302

Physics Subject Headings (PhySH)

Heat radiation Heat transfer Phonons Polaritons Thermal conductivity

Nanostructures Semiconductor compounds

Calorimetry Drude model Methods in transport Numerical techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shen Yan ^1,*, Yuxuan Luan ^1,*, Ju Won Lim ², Rohith Mittapally ¹, Amin Reihani ¹, Zhongyong Wang ¹, Yoichiro Tsurimaki ³, Shanhui Fan ^3,†, Pramod Reddy ^1,2,‡, and Edgar Meyhofer ^1,§

¹Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
²Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
³Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

^*These authors contributed equally to this work.
^†Corresponding author: shanhui@stanford.edu
^‡Corresponding author: pramodr@umich.edu
^§Corresponding author: meyhofer@umich.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 131, Iss. 19 — 10 November 2023

Reuse & Permissions

Access Options

Article part of CHORUS

Accepted manuscript will be available starting 8 November 2024.

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic of the NFRHT measurement platform integrated into a variable temperature scanning probe instrument and scanning electron microscopy (SEM) images of the employed devices. (a) Emitter (bottom) and a receiver (with integrated sphere, top). The silicon-based emitter has an integrated Pt heater and a $15 μ m$ -tall mesa that is coated with a $2 μ m$ -thick ${SiO}_{2}$ layer. The receiver consists of an integrated Pt resistance sensor and a $70 μ m$ -diameter silica sphere. The heat current ( $Q_{radiation}$ ) is measured by modulating the emitter temperature via an ac current ( $I_{ac, heating}$ ) supplied to the integrated Pt line and measuring the resulting temperature oscillations of the receiver by supplying a dc current ( $I_{dc, sensing}$ ) to its Pt thermometer. The gap size between the emitter and the receiver is controlled via a piezo actuator. (b) SEM image of the receiver with integrated sphere. (c) SEM image of the emitter featuring a Pt sensor (blue) and the ${SiO}_{2}$ -coated mesa (brown).
Reuse & Permissions
Figure 2
Experimental approach for probing NFRHT at cryogenic temperatures. (a) Data obtained in a measurement performed at 100 K. The top panel shows how the separation between the receiver and the emitter is varied, via a piezoelectric actuator, in steps of $\sim 0.8 nm$ . The bottom panel depicts the measured temperature rise of the receiver as a function of gap size. Contact between the emitter and the receiver is signaled by a jump in the temperature (marked red) of the receiver. (b) Thermal resistance network of the radiative heat transfer between the emitter and the receiver. (c) Measured thermal conductance with error bars as a function of gap size. To increase the range, we spliced two high resolution gap conductance records. The overlapping region of the conductances (see inset) enables us to concatenate the data. (d) Schematic description of the process of concatenation. The first approach contains information till contact. The second approach starts by retracting the receiver by a coarse positioner. Subsequently, the receiver device was displaced towards the emitter until heat flux signal exceeded the smallest signal measured in the first approach.
Reuse & Permissions
Figure 3
Gap size and temperature dependence of near-field thermal conductance. (a) Measured near-field thermal conductance as a function of gap size at different temperatures for an emitter device coated with a $2 μ m$ -thick layer of ${SiO}_{2}$ and a receiver device with a $70 μ m$ -diameter ${SiO}_{2}$ sphere. The inset depicts the temperature dependence of near-field thermal conductance (normalized to the value at 300 K) at various gap sizes using the data from panel (a). The two dashed lines represent the expected conductance following $T^{3}$ and $T^{2}$ temperature dependence. (b) The spectral heat flux for silica surfaces in the near-field [geometry corresponds to that shown in the inset of (c) for a gap size of 20 nm]. The spectral heat flux between two semi-infinite blackbodies in the far-field of each other is shown in the inset. (c) The computational results of the temperature-dependent NFRHT in the plane-plane geometry using fluctuational electrodynamics (inset shows the geometry that is modeled). (d) Computational results for the gap-dependent NFRHT, at various temperatures, in the sphere-plane geometry using the Derjaguin approximation (inset illustrates the Derjaguin approximation method). The computed values were scaled as described in the main text. Note that most of the error bars shown in panel (a) and (d) are smaller than the symbols.
Reuse & Permissions
Figure 4
Illustration of the origin of the observed temperature dependence. (a) Comparison of experimental data with various computational and analytical models. Computational results for the plane-plane structure show the same temperature dependence as experimental data but deviate from a $T^{3}$ dependence, which holds for far-field radiative heat transfer. See details of the models in [38]. (b) The dispersion relation at different gap sizes between two ${SiO}_{2}$ planes. (c) The integrated transmission as a function of energy. The two SPhP-resonant peaks are fitted by two Lorentzian functions shown by dashed lines. (d) Dashed lines represent the fitted analytical model based on Eq. (3) and (S33), which incorporate a temperature-dependent dielectric function. The experimental data and model are in good agreement (most of the error bars are smaller than the symbols). Additional details in the Supplemental Material [38].
Reuse & Permissions

Physical Review Letters